Information on Result #717963
Linear OA(980, 124, F9, 41) (dual of [124, 44, 42]-code), using construction XX applied to C1 = C([9,41]), C2 = C([1,29]), C3 = C1 + C2 = C([9,29]), and C∩ = C1 ∩ C2 = C([1,41]) based on
- linear OA(950, 80, F9, 33) (dual of [80, 30, 34]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {9,10,…,41}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(944, 80, F9, 29) (dual of [80, 36, 30]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(934, 80, F9, 21) (dual of [80, 46, 22]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {9,10,…,29}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(914, 28, F9, 11) (dual of [28, 14, 12]-code), using
- extended algebraic-geometric code AGe(F,16P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- extended algebraic-geometric code AGe(F,16P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- linear OA(98, 16, F9, 7) (dual of [16, 8, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(98, 18, F9, 7) (dual of [18, 10, 8]-code), using
- 2 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- 2 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(98, 18, F9, 7) (dual of [18, 10, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(980, 62, F9, 2, 41) (dual of [(62, 2), 44, 42]-NRT-code) | [i] | OOA Folding | |